We interpret spectral clustering
algorithms in the light of unsupervised learning techniques like
principal component analysis and kernel principal component analysis.
We show both are equivalent up to a normalization of the do product or
the affinity matrix.

Given a large number of articles
comprising of natural text we intend to train on the text and extract
clusters of words which are semantically related. When we query the
system with a word it will return all the words which are very related
to the same theme. For example our training set could be all the
articles appearing in a magazine. If I query the system with war it
would return all the words like soldiers, aircrafts, Iraq etc. Note
that all the words do not mean the same they are related by a common
unifying theme of war. We want to apply the techniques of nonlinear
manifold learning to this unsupervised learning task. We experimented
with two techniques, a linear technique Principal Component Analysis
and and non-linear manifold learning technique called Isomap.

We
present a perceptually inspired mapping to convert a simple two
dimensional image consisting of simple geometrical shapes to a one
dimensional audio waveform consisting of simple harmonic complexes.
More specifically we map objects to harmonic complexes where the pitch,
timbre and location of the complex corresponds to the size, shape and
the position of the object respectively.

The aim of this
report is to study the two nonlinear manifold learning techniques
recently proposed [Isomap and Locally Linear
Embedding (LLE)] and suggest directions for further research. First the
Isomap and the LLE algorithm are discussed in detail. Some of the areas
that need further work are pointed out. A few novel applications which
could use these two algorithms have been discussed.

PDMA-MEMORY ANALYSIS TOOLKIT

We developed a tool
can be used to test programs for memory bottlenecks such as cache
misses. The tool uses underlying hardware counters supported by
existing machines to monitor memory-specific events and patches the
runtime code of the program in order to monitor these events. The
performance analysis results are displayed using histograms and stacked
bar charts that are hyperlinked with the original source code. We use
our tool to conduct tests on specific benchmarks such as Parkbench and
FFT that successfully demonstrate its application utility.

Sound source
Localization can be formulated as a non linear least squares problem.
In this project we evaluated different minimization methods including
Nelder Mead simplex method, Quasi Netwton methods, Leveneberg
Marquadrat algorithm and the Gauss Newton algorithm. Gauss Newton
method was the best in terms of localization eroor and the number of
iterations required.

The
aim of our project was to detect and localize human faces in any given
grayscale image. In this project we evaluated
the performance of different approaches for face detection on
gray scale images including Neural networks, Principal Component
Analysis(PCA), Kernel PCA, Linear Discriminant Analysis(LDA), Kernel
LDA, Biased Discriminant Analysis(BDA), Kernel BDA and Adaboost. We
also combined the above a approaches with a skin color detector to
speed up the algorithm.

A Video Codec has
been implemented using transform coding for reduction of spatial
redundancy and unidirectional prediction to reduce
temporal redundancy. Coding decisions [I/P frame, Intra/Inter Macro
block] are adaptively made to ensure best tradeoff between quality and
compression. Shot segmentation is an important step in video content
analysis. The automatic partitioning of video into shots involves the
detection of transitions. Detecting transitions by extracting the DC
image in the compressed domain is advantageous. In this report we
extract the DC images from the compressed MPEG stream . We implement
the algorithms for cut and wipe detection . We also propose a new
algorithm for wipe detection.

PROBABILITY DENSITY
ESTIMATION

The
aim of the project was to estimate the probability density function
(PDF) of any arbitrary distribution from a set of training samples. PDF
estimation was done using parametric (Maximum Likelihood estimation of
a Gaussian model), non-parametric (Histogram, Kernel based and
K-nearest neighbor) and semi-parametric methods (EM algorithm and
gradient based optimization). Application of EM algorithm for binary
sequence estimation has also been discussed.

LINEAR NETWORKS, MULTILAYER PERCEPTRONS AND RBF'S

The
aim of the project was to implement a Linear network (LN) for a 3 class
pattern classification problem. Training was done using the LMS
algorithm. A 3-h-1 Multi Layer Perceptron (MLP) was implemented for a
two class problem. Back propagation was used for training. The network
was then pruned using Optimal Brain Surgeon. A Radial Basis Function
(RBF) network using Inverse multiquadratic basis function was
implemented for function approximation. The training was done using LMS
algorithm. Also an MLP was designed and implemented for printed numeral
recognition.

The aim of the project
was to study the different beamforming techniques and use the
Constrained Least Mean Squares (LMS) filter for spatial filtering. A
Constrained least mean square algorithm (also known as Frost
Beamformer) was derived which is capable of iteratively adapting the
weights of the sensor array to minimize noise power at the array output
while maintaining a chosen frequency response in the look direction. It
was observed that there was a significant improvement in the SNR as
compared to the simple delay and sum beamformer.The beamformers were
also implemented in real time using two circular arrays of 7
microphones each.